删失分位数回归模型中的多变点估计

doi:10.6040/j.issn.1671-9352.0.2024.021

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (2): 96-104.doi: 10.6040/j.issn.1671-9352.0.2024.021

• • 上一篇

删失分位数回归模型中的多变点估计

李学文¹,冯可馨²,王小刚^2*

1.北方民族大学商学院, 宁夏银川 750021;2.北方民族大学数学与信息科学学院, 宁夏银川 750021

发布日期:2025-02-14
通讯作者: 王小刚(1980— ),男,教授,博士,研究方向为复杂数据统计推断、风险管理. E-mail:wangxg9102@163.com
作者简介:李学文(1980— ),女,讲师,博士,研究方向为风险管理. E-mail:421630014@qq.com
基金资助:
宁夏自然科学基金重点项目(2023AAC02043);全国统计科学研究项目(2023LY070);宁夏高等教育一流学科建设基金资助项目(NXYLXK2017B09)

Estimation of multiple change points for censored quantile regression model

LI Xuewen¹, FENG Kexin², WANG Xiaogang^2*

1. School of Business, North Minzu University, Yinchuan 750021, Ningxia, China;
2. School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, Ningxia, China

Published:2025-02-14

摘要/Abstract

摘要： 针对删失分位数回归模型中的变点个数、位置及模型参数同时估计问题,基于线性化技术得到参数的有效估计,消除目标函数不可导与非凸的困难。该方法能捕捉响应变量受到某一协变量的影响而存在的多个变点,能更好理解复杂非线性关系的同时保持较快的收敛速度,兼顾灵活性与可解释性。数值模拟验证估计方法在不同分位点、同(异)方差情形下具备有效性和稳健性,实证分析发现存在2个变点,并对其进行解释。

关键词: 多变点估计, 删失数据, 分位数回归模型, 线性化技术

Abstract: To simultaneously estimate the number of change points, the location of change points and the model parameters in censored quantile regression model, a linearization technique is employed to obtain estimators for above parameters. This approach overcomes the issues of non-differentiability and non-convexity objective function at the change points. It is capable of capturing the relationship between response and covariate of interest that changes across multiple change points. Furthermore, the proposed estimators strike a balance between flexibility and interpretability, making them become a useful tool for identifying and explaining change points. Simulation studies show that the estimators demonstrate robustness in both homoscedastic and heteroscedastic conditions across various quantile levels. An empirical analysis reveals the existence of two change points and their change point effects.

Key words: estimation multiple change point, censored data, quantile regression model, linearization technique

中图分类号:

O212.2

李学文,冯可馨,王小刚. 删失分位数回归模型中的多变点估计[J]. 《山东大学学报(理学版)》, 2025, 60(2): 96-104.

LI Xuewen, FENG Kexin, WANG Xiaogang. Estimation of multiple change points for censored quantile regression model[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(2): 96-104.

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删失分位数回归模型中的多变点估计

Estimation of multiple change points for censored quantile regression model

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